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        <td class="header">&nbsp; Orthorectification</td>
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<h3>Range Doppler Terrain Correction Operator</h3>

<p>Due to topographical variations of a scene and the tilt of the satellite
    sensor, distances can be distorted in the SAR images. Image data not directly
    at the sensor&#8217;s Nadir location will have some distortion. Terrain corrections
    are intended to compensate for these distortions so that the geometric
    representation of the image will be as close as possible to the real world.</p>

<p class="Paranum"><span style="" lang="EN-CA"><span style=""><span style="font-family: &quot;Times New Roman&quot;; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal;"></span></span></span>The
    geometry of topographical
    distortions in SAR imagery is shown below<span lang="EN-CA"><span style=""></span></span><span lang="EN-CA">.<span style="">&nbsp; </span>Here we can see that point <b>B</b> with elevation <b>h</b> above the ellipsoid is imaged at position </span><b><span style="font-family: Symbol;" lang="EN-CA">B</span><span lang="EN-CA">&#8217;</span></b><span lang="EN-CA"> in SAR image, though its real position is <b>B"</b>.<span style="">&nbsp; </span>The offset&nbsp;</span><b><span style="font-family: Symbol;" lang="EN-CA"><span style="">&#916;</span></span><sub><span lang="EN-CA">r</span></sub></b><b><span style="font-family: Symbol;" lang="EN-CA"> </span></b><span lang="EN-CA">between </span><b><span style="font-family: Symbol;" lang="EN-CA">B</span><span lang="EN-CA">'</span></b><span lang="EN-CA"> and <b>B"</b> </span><span style="font-family: Symbol;" lang="EN-CA"><span style="">&nbsp;</span></span><span lang="EN-CA">exhibits the effect of topographic distortions.</span></p>

<div style="text-align: center;"><b><span style="font-size: 10pt; font-family: &quot;Times New Roman&quot;;" lang="EN-CA"></span></b><span style="font-weight: bold;"><img style="width: 377px; height: 263px;" alt="" src="images/sar_geometry.png"></span></div>
<p class="Paranum"><span lang="EN-CA"> </span></p>


<p>Terrain Correction allows geometric overlays of data from different sensors
    and/or geometries.</p><h4>Orthorectification Algorithm</h4>

<p>The
    Range Doppler Terrain Correction Operator implements the Range Doppler
    orthorectification method [1] for geocoding SAR images from single 2D
    raster radar geometry. It uses available orbit
    state
    vector information in the metadata or <a href="ApplyOrbitFileOp.html">external
        precise orbit</a> (only for ERS and ASAR), the radar timing annotations, the slant to ground range
    conversion parameters together with the reference DEM data to derive the precise
    geolocation information.&nbsp;</p><h4>DEM Supported</h4>

<p>Currently, only the DEMs with geographic coordinates (P<sub>lat</sub>, P<sub>lon</sub>, P<sub>h</sub>) referred to
    global geodetic ellipsoid reference WGS84 (and height in meters) are properly supported.</p>

<p>Various different types of Digital Elevation
    models can be used (ACE, GETASSE30,&nbsp;ASTER, SRTM 3Sec&nbsp;GeoTiff).</p><p>The
STRM v.4 (3&#8221; tiles) from the Joint Research Center FTP (xftp.jrc.it)
will automatically be downloaded in tiles for&nbsp; the area covered by
the image to be orthorectified. The tiles will be downloaded to the
folder .snap\AuxData\DEMs\SRTM_DEM\tiff. The .snap folder is located in
your user folder.</p>



<p>Please
    note that for ACE and SRTM, the height information (being referred to
    geoid EGM96) is automatically corrected to obtain height relative to
    the WGS84 ellipsoid. For Aster Dem height correction is not yet
    applied. </p>

<p>Note also that the SRTM DEM covers area between -60
    and 60 degrees latitude. Therefore, for orthorectification of product
    of high latitude area, different DEM should be used. </p>

<p>User can also use external DEM file in Geotiff format which, as specified above, must be with geographic coordinates&nbsp;(P<sub>lat</sub>,
    P<sub>lon</sub>, P<sub>h</sub>) referred to global geodetic ellipsoid reference WGS84 (and height in meters).</p>
<h4>Pixel Spacing</h4>

<p>Besides
    the default suggested pixel spacing computed with parameters in the
    metadata, user can specify output pixel spacing for the orthorectified
    image.</p>

<p> The
    pixel spacing can be entered in both meters and degrees. If the pixel
    spacing in one unit is entered, then &nbsp;the pixel spacing in another
    unit is computed
    automatically.</p>

<p> The calculations of the pixel spacing in meters and in
    degrees&nbsp;are given by the following equations:&nbsp;<span style="font-size: 11pt; font-family: &quot;Times New Roman&quot;;" lang="EN-GB"></span><i><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;" lang="EN-GB"></span></i><span style="font-size: 7pt; font-family: Symbol;" lang="EN-GB"></span><i><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;" lang="EN-GB"></span></i><span style="font-size: 7pt; font-family: Symbol;" lang="EN-GB"></span><i><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;" lang="EN-GB"></span><span style="font-size: 8pt; font-family: &quot;Times New Roman&quot;;" lang="EN-GB"></span></i><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;" lang="EN-GB"></span></p>

<p style="margin-left: 40px;">pixelSpacingInDegree = pixelSpacingInMeter / EquatorialEarthRadius * 180 / PI;</p>

<p style="margin-left: 40px;">pixelSpacingInMeter = pixelSpacingInDegree * PolarEarthRadius&nbsp; * PI / 180;</p>

<p>where&nbsp;EquatorialEarthRadius = 6378137.0 m and PolarEarthRadius = 6356752.314245 m as given in WGS84.&nbsp;</p><h4>Radiometric Normalization</h4>

<p>This option implements a radiometric normalization based on the approach proposed by Kellndorfer et al., TGRS, Sept.
    1998 where <br><img style="width: 233px; height: 67px;" alt="" src="images/range_doppler_eq5.jpg"></p>

<p>In current implementation <span style="font-style: italic;">&#952;</span><sub style="font-style: italic;">DEM</sub>
    is the local incidence angle projected into the range plane and defined
    as the angle between the incoming radiation vector and the projected
    surface normal vector into range plane[2]. The range plane is the plane
    formed by the satellite position, backscattering element position and
    the earth centre.&nbsp;</p>

<p>Note that among&nbsp;<span style="font-style: italic;">&#963;</span><sup style="font-style: italic;"><sub>0</sub></sup>, <span style="font-style: italic;">&#947;</span><sup style="font-style: italic;"><sub>0</sub></sup> and <span style="font-style: italic;">&#946;</span><sup style="font-style: italic;"><sub>0</sub></sup> bands output in the target product, only&nbsp;<span style="font-style: italic;">&#963;</span><sup style="font-style: italic;"><sub>0</sub></sup> is real band while
    <span style="font-style: italic;">&#947;</span><sup style="font-style: italic;"><sub>0</sub></sup> and <span style="font-style: italic;">&#946;</span><sup style="font-style: italic;"><sub>0</sub></sup> are virtual
    bands expressed in terms of <span style="font-style: italic;">&#963;</span><sup style="font-style: italic;"><sub>0</sub></sup>&nbsp;and incidence angle. Therefore, <span style="font-style: italic;">&#963;</span><sup style="font-style: italic;"><sub>0</sub></sup>&nbsp;and
    incidence angle are automatically saved and output if <span style="font-style: italic;">&#947;</span><sup style="font-style: italic;"><sub>0</sub></sup> or <span style="font-style: italic;">&#946;</span><sup style="font-style: italic;"><sub>0</sub></sup> is selected.</p>

<p>For <span style="font-style: italic;">&#963;</span><sup style="font-style: italic;"><sub>0</sub></sup> and <span style="font-style: italic;">&#947;</span><sup style="font-style: italic;"><sub>0</sub></sup>&nbsp;calculation,
    by default the projected local incidence angle from DEM [2] (local
    incidence angle projected into range plane) option is selected, but the
    option of incidence angle from ellipsoid correction (incidence angle
    from tie points of the source product) is also available.<br></p><h4>ENVISAT ASAR</h4>

<p>
    The correction factors [3] applied to the original image depend on if
    the product is complex or detected and&nbsp;the selection of Auxiliary
    file (ASAR XCA file).&nbsp;</p><h4>Complex Product (IMS, APS)</h4>
<ul>
    <li><span style="font-weight: bold;">Latest AUX File</span>&nbsp;(&amp; use projected local incidence angle computed
        from DEM):<p>&nbsp;The
            most recent ASAR XCA available from installation_folder\auxdata\envisat compatible with product date is
            automatically selected. According to this XCA file, calibration
            constant, range spreading loss and antenna pattern gain are obtained.</p></li>
    <ul>
        <li><span style="text-decoration: underline;">Applied factors</span>:</li>
    </ul>
    <ul>
        <ol>
            <li><p>apply projected local incidence angle into the range plane correction</p></li>
            <li><p>apply calibration constant correction based on the XCA file<br></p></li>
            <li><p>apply range spreading loss correction based on the XCA file and DEM geometry<br></p></li>
            <li><p>apply antenna pattern gain correction based on the XCA file and DEM geometry<br></p></li>
        </ol>
    </ul>
    <li><span style="font-weight: bold;">External AUX File</span>&nbsp;(&amp; use projected local incidence angle
        computed from DEM):<p>&nbsp;User
            can select a specific ASAR XCA file available from the installation folder or from another repository.
            According to
            this selected XCA file, calibration constant, range spreading loss and
            antenna pattern gain are computed.</p></li>
    <ul>
        <li><span style="text-decoration: underline;">Applied factors</span>:</li>
    </ul>
    <ul>
        <ol>
            <li><p>apply projected local incidence angle into the range plane correction</p></li>
            <li><p>apply calibration constant correction based on the selected XCA file<br></p></li>
            <li><p>apply range spreading loss correction based on the selected XCA file and DEM geometry<br></p></li>
            <li><p>apply antenna pattern gain correction based on the selected XCA file and DEM geometry<br></p></li>
        </ol>
    </ul>
</ul>
<h4>Detected Product (IMP, IMM, APP, APM, WSM)</h4>
<ul>
    <li><span style="font-weight: bold;">Latest AUX File</span>&nbsp;(&amp; use projected local incidence angle computed
        from DEM):<p>The
            most recent ASAR XCA available from the installation folder compatible with product date is
            automatically selected. Basically with this option all the correction
            factors applied to the original SAR image based on product XCA file
            used during the focusing, such as antenna pattern gain and range
            spreading loss, are removed first. Then new factors computed according
            to the new ASAR XCA file together with calibration constant and local
            incidence angle correction factors are applied during the radiometric
            normalisation process.</p></li>
    <ul>
        <li><span style="text-decoration: underline;">Applied factors</span>:</li>
    </ul>
    <ul>
        <ol>
            <li><p>remove antenna pattern gain correction based on product XCA file</p></li>
            <li><p>remove range spreading loss correction based on product XCA file<br></p></li>
            <li><p>apply projected local incidence angle into the range plane correction<br></p></li>
            <li><p>apply calibration constant correction based on new XCA file</p></li>
            <li><p>apply range spreading loss correction based on new XCA file and DEM geometry</p></li>
            <li><p>apply new antenna pattern gain correction based on new XCA file and DEM geometry<br></p></li>
        </ol>
    </ul>
    <li><span style="font-weight: bold;">Product AUX File</span>&nbsp;(&amp; use projected local incidence angle
        computed from DEM):<p>&nbsp;The
            product ASAR XCA file employed during the focusing is used. With this
            option the antenna pattern gain and range spreading loss are kept from
            the original product and only the calibration constant and local
            incidence angle correction factors are applied during the radiometric
            normalisation process.</p></li>
    <ul>
        <li><span style="text-decoration: underline;">Applied factors</span>:</li>
    </ul>
    <ul>
        <ol>
            <li><p>apply projected local incidence angle into the range plane correction</p></li>
            <li><p>apply calibration constant correction based on product XCA file<br></p></li>
        </ol>
    </ul>
</ul>
<ul>
    <li><span style="font-weight: bold;">External AUX File</span>&nbsp;(&amp; use projected local incidence angle
        computed from DEM):<p>&nbsp;User
            can select a specific ASAR XCA file available from the installation folder or from another repository.
            Basically with
            this option all the correction factors applied to the original SAR
            image based on product XCA file used during the focusing, such as
            antenna pattern gain and range spreading loss, are removed first. Then
            new factors computed according to the new selected ASAR XCA file
            together with calibration constant and local incidence angle correction
            factors are applied during the radiometric normalisation process.</p></li>
    <ul>
        <li><span style="text-decoration: underline;">Applied factors</span>:</li>
    </ul>
    <ul>
        <ol>
            <li><p>remove antenna pattern gain correction based on product XCA file</p></li>
            <li><p>remove range spreading loss correction based on product XCA file<br></p></li>
            <li><p>apply projected local incidence angle into the range plane correction<br></p></li>
            <li><p>apply calibration constant correction based on new selected XCA file</p></li>
            <li><p>apply range spreading loss correction based on new selected XCA file and DEM geometry</p></li>
            <li><p>apply new antenna pattern gain correction based on new selected XCA file and DEM geometry<br></p>
            </li>
        </ol>
    </ul>
</ul>
<p>
    Please note that if the product has been previously multilooked then
    the radiometric normalization does not correct the antenna pattern and
    range spreading loss and only constant and incidence angle corrections
    are applied. This is because the original antenna pattern and the range
    spreading loss correction cannot be properly removed due to the pixel
    averaging by multilooking. <br></p>

<p>If
    user needs to apply a radiometric normalization, multilook and terrain
    correction to a product, then user graph
    &#8220;RemoveAntPat_Multilook_Orthorectify&#8221; could be used.<br></p><h4>ERS 1&amp;2</h4>

<p>For ERS 1&amp;2 the radiometric normalization cannot be applied directly to original ERS product.<br></p>

<p>Because
    of the Analogue to Digital Converter (ADC) power loss correction , a
    step before is required to properly handle the data. It is necessary to
    employ the Remove Antenna Pattern Operator which performs the following
    operations:</p>

<p>&nbsp;For Single look complex (SLC, IMS) products<br></p>
<ul>
    <li>apply ADC correction</li>
</ul>
<p>For Ground range (PRI, IMP) products:</p>
<ul>
    <li>remove antenna pattern gain</li>
    <li>remove range spreading loss</li>
    <li>apply ADC correction<span style="font-weight: bold;"></span></li>
</ul>
<p>After
    having applied the Remove Antenna Pattern Operator to ERS data, the
    radiometric normalisation can be performed during the Terrain
    Correction.<br></p>

<p>The applied factors in case of "USE projected angle from the DEM" selection are:<br></p>
<ol>
    <li>apply projected local incidence angle into the range plane correction</li>
    <li>apply absolute calibration constant correction</li>
    <li>apply range spreading loss correction based on product metadata and DEM geometry</li>
    <li>apply new antenna pattern gain correction based on product metadata and DEM geometry</li>
</ol>
<p>To apply radiometric normalization and terrain correction for ERS, user can also use one of the following user
    graphs:<br></p>
<ul>
    <li>RemoveAntPat_Orthorectify</li>
    <li>RemoveAntPat_Multilook_Orthorectify</li>
</ul>
<h4>RADARSAT-2</h4>
<ul>
    <li>In
        case of "USE projected angle from the DEM" selection, the radiometric
        normalisation is performed applying the product LUTs and multiplying by
        (sin &#61553;DEM/sin &#61553;el), where &#61553;DEM is projected local incidence angle into
        the range plane and &#61553;el is the incidence angle computed from the tie
        point grid respect to ellipsoid.
    </li>
    <li>In case of selection of "USE
        incidence angle from Ellipsoid", the radiometric normalisation is
        performed applying the product LUT.
    </li>
</ul>
<p>These LUTs allow one to
    convert the digital numbers found in the output product to
    sigma-nought, beta-nought, or gamma-nought values (depending on which
    LUT is used).<br></p><h4>TerraSAR-X</h4>
<ul>
    <li>In case of "USE projected angle from the DEM" selection, the radiometric normalisation is performed applying<br>
        <ol>
            <li>projected local incidence angle into the range plane correction</li>
            <li>absolute calibration constant correction</li>
        </ol>
    </li>
    <li>In case of " USE incidence angle from Ellipsoid " selection, the radiometric normalisation is performed applying<br>
        <ol>
            <li>projected local incidence angle into the range plane correction</li>
            <li>absolute calibration constant correction</li>
        </ol>
    </li>
</ul>
Please note that the simplified approach&nbsp; where Noise Equivalent Beta Naught is neglected has been implemented.<br>
<h4>Cosmo-SkyMed</h4>
<ul>
    <li>In case of "USE projected angle from the DEM" selection, the radiometric normalisation is performed deriving
        <span style="font-style: italic;">&#963;</span><sup style="font-style: italic;"><sub>0</sub></sup><sub style="font-style: italic;">Ellipsoid</sub> [7] and then multiplying by (sin<span style="font-style: italic;">&#952;</span><sub style="font-style: italic;">DEM</sub> /&nbsp;sin<span style="font-style: italic;">&#952;</span><sub style="font-style: italic;">el</sub>), where <span style="font-style: italic;">&#952;</span><sub style="font-style: italic;">DEM</sub>&nbsp;is the
        projected local incidence angle into the range plane and <span style="font-style: italic;">&#952;</span><sub style="font-style: italic;">el</sub>&nbsp;is the incidence angle computed from the tie point grid
        respect to ellipsoid.
    </li>
    <li>In case of selection of "USE incidence angle from Ellipsoid", the radiometric normalisation is performed
        deriving <span style="font-style: italic;">&#963;</span><sup style="font-style: italic;"><sub>0</sub></sup><sub style="font-style: italic;">Ellipsoid</sub> [7] <br></li>
</ul>
<span style="text-decoration: underline; font-weight: bold;">Definitions:</span><br>
<ol>
    <li>The
        local incidence angle is defined as the angle between the normal vector
        of the backscattering element (i.e. vector perpendicular to the ground
        surface) and the incoming radiation vector (i.e. vector formed by the
        satellite position and the backscattering element position) [2].
    </li>
    <li>The
        projected local incidence angle from DEM is defined as the angle
        between the incoming radiation vector (as defined above) and the
        projected surface normal vector into range plane. Here range plane is
        the plane formed by the satellite position, backscattering element
        position and the earth centre [2].<br></li>
</ol>
<h4>Parameters Used</h4>

<p>
    The following&nbsp;parameters are used by the operator:
</p>
<ol>
    <li>Source Band: All bands (real or virtual) of the source product. User can
        select one or more bands for calibration. If no bands are selected, then by
        default all bands are used.
    </li>
    <li>Digital Elevation Model: DEM types. Please refer to <span style="font-weight: bold;">DEM Supported</span>
        section above.
    </li>
    <li>External DEM: User specified external DEM file. Currently only DEM in Geotiff format with geographic coordinates
        (P<sub>lat</sub>, P<sub>lon</sub>, P<sub>h</sub>) referred to global geodetic ellipsoid reference WGS84 (and
        height in meters)&nbsp;is accepted.
    </li>
    <li>DEM Resampling Method: Interpolation method for obtaining elevation values
        from the original DEM file. The following interpolation methods are available:
        nearest neighbour, bi-linear, cubic convolution, bi-sinc and bi-cubic interpolations.
    </li>
    <li>Image Resampling Method: Interpolation methods for obtaining pixel values
        from the source image. The following interpolation methods are available:
        nearest neighbour, bi-linear, cubic and bi-sinc interpolations.
    </li>
    <li>Pixel Spacing (m): User can specify pixel spacing&nbsp;in meters for orthorectified
        image. If no pixel spacing is specified, then default&nbsp;pixel spacing
        computed from the source SAR image is used. For details, the reader is referred to <span style="font-weight: bold;">Pixel Spacing</span> section above.
    </li>
    <li>Pixel Spacing (deg): User
        can also specify the pixel spacing&nbsp;in degrees. &nbsp;If the value
        of any of the two pixel spacing is changed, the other one is updated
        automatically.&nbsp;For details, the reader is referred to <span style="font-weight: bold;">Pixel Spacing</span>
        section above.
    </li>
    <li>Map
        Projection: The map projection types.&nbsp;By default the output
        image will be expressed in WGS84 latlong geographic coordinate.
    </li>
    <li>Save DEM as a band: Checkbox indicating that DEM will be saved as a band in the
        target product.
    </li>
    <li>Save local incidence angle as a band: Checkbox indicating that local incidence
        angle will be saved as a band in the target product.
    </li>
    <li>Save projected (into the range plane) local incidence angle as a band: Checkbox indicating that the
        projected local incidence angle will be saved as a band in the target product.
    </li>
    <li>Save selected source band: Checkbox indicating that orthorectified
        images of user selected bands will be saved without applying
        radiometric normalization.
    </li>
    <li>Apply radiometric normalization: Checkbox indicating that radiometric normalization will be applied to the
        orthorectified image.
    </li>
    <li>Save Sigma0 as a band: Checkbox indicating that sigma0 will be
        saved as a band in the target product. The Sigma0 can be generated
        using projected local incidence angle, local incidence angle or incidence angle from
        ellipsoid.
    </li>
    <li>Save
        Gamma0 as a band: Checkbox indicating that Gamma0 will be saved as a
        band in the target product. The Gamma0 can be generated using projected
        local incidence angle, local incidence angle or incidence angle from ellipsoid.
    </li>
    <li>Save Beta0 as a band: Checkbox indicating that Beta0 will be saved as a band in the target product.</li>
    <li>Auxiliary
        File: available only for ASAR. User selected ASAR XCA file for radiometric normalization. The
        following options are available: <span style="font-weight: bold;">Latest Auxiliary File</span>, <span style="font-weight: bold;">Product
Auxiliary
File</span> (for detected product only) and <span style="font-weight: bold;">External Auxiliary File</span>. By
        default,&nbsp;the Latest Auxiliary
        File&nbsp;is used. Details about the corrections applied according to the XCA selection are provided in <span style="font-weight: bold;">Radiometric Normalisation</span> &#8211; Envisat ASAR section above.
    </li>
</ol>
<i ,j="">
<br></i><p><i ,j=""><img style="width: 500px; height: 607px;" alt="" src="images/range_doppler_dlg.JPG"><br></i></p>

<p><i ,j="">
    </i></p>

<p style="font-weight: bold;"><i ,j=""> Reference:</i></p>

<p> [1] Small D., Schubert A.,&nbsp;Guide to ASAR Geocoding, RSL-ASAR-GC-AD, Issue 1.0, March 2008</p>

<p>[2]&nbsp;Schreier G., SAR Geocoding: Data and Systems, Wichmann 1993</p>


<p>[3] Rosich B., Meadows P., Absolute calibration of ASAR Level 1 products,
    ESA/ESRIN, ENVI-CLVL-EOPG-TN-03-0010, Issue 1, Rev. 5, October 2004</p>

<p>[4]
    Laur H., Bally P., Meadows P., S�nchez J., Sch�ttler B., Lopinto E.
    &amp; Esteban D., ERS SAR Calibration: Derivation of &#963;0 in ESA ERS SAR
    PRI Products, ESA/ESRIN, ES-TN-RS-PM-HL09, Issue 2, Rev. 5f, November
    2004&nbsp;</p>

<p>[5] RADARSAT-2 PRODUCT FORMAT DEFINITION - RN-RP-51-2713 Issue 1/7: March 14, 2008</p>

<p>[6] Radiometric Calibration of TerraSAR-X data - TSXX-ITD-TN-0049-radiometric_calculations_I1.00.doc, 2008</p>

<p>[7] For further details about Cosmo-SkyMed calibration please contact Cosmo-SkyMed Help Desk at&nbsp;<small><small><font color="black" face="Arial" size="2"><small><small><span style="font-size: 10pt; font-family: Arial;" lang="EN-GB"><a href="mailto:info.cosmo@e-geos.it" moz-do-not-send="true">info.cosmo@e-geos.it</a></span></small></small></font></small></small></p>
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